The main components of my research activities are statistical methodological research and scientific collaborative research. My statistical methodological research concerns developing statistical methodology for analyzing spatially referenced data (spatial statistics) and spatial data repeatedly sampled over time (spatio-temporal statistics), that arise often in the biological, physical, and social sciences. My collaborative research concerns applying modern statistical methods, especially spatial and spatio-temporal statistics, to studies of agricultural, biological, ecological, environmental, and social systems conducted by research scientists. To a large extent, my overall research program involves a close connection between the two types of research activities: Problems in my collaborative research that do not have adequate statistical tools motivate my statistical methodological research; whereas the new methods I develop in statistical methodological research are applied in my collaborative projects.

Research Category:
Statistics

Courses Taught:

Statistics 571: Statistical Methods for Bioscience I

Statistics 572: Statistical Methods for Bioscience II

Statistics 575: Statistical Methods for Spatial Data

Statistics 992: Statistics for Spatial Data: Theory and Methods

Statistics 998: Statistical Consulting

Affiliations:

Department of Statistics
Department of Entomology
Biometry Program, College of Agricultural and Life Sciences

Tracey, J.A., Zhu, J., and Crooks, K. (2005). A set of nonlinear regression models for animal movement in response to a single landscape feature. Journal of Agricultural, Biological, and Environmental Statistics, 10, 1–18.

Research

Resampling Methods:

Earlier in my career, I worked on asymptotic inference for spatial cumulative distribution functions using spatial subsampling with application to environmental monitoring and assessment (Zhu et al. 2001, 2002). I then investigated spatial resampling methods. On the one hand, I worked on the theory of the spatial block bootstrap, which is a resampling method alternative to spatial subsampling (Lahiri and Zhu 2006; Zhu and Lahiri 2007). On the other hand, motivated by my collaborative research work with Dr. G. Morgan in Horticulture on the population dynamics of root lesion nematodes in potato fields (Morgan et al. 2002a, 2002b), I developed new statistical methodology based on the theory of the spatial block bootstrap. In particular, I developed a spatial block bootstrap for comparing spatial variables in different subregions (Zhu and Morgan 2004a) and for comparing spatial variables over time (Zhu and Morgan 2004b).

Spatio-Temporal Statistics:

I have collaborated with Drs. K. Raffa, B. Aukema, and their research groups in Forest Entomology on population dynamics and interactions among trees, insects, and fungi in forest stands of Wisconsin. The nature of the data is complex, involving spatial, temporal, and multiple response variables that are not necessarily normally distributed, which motivated me to pursue research in spatial-temporal statistics involving statistical methodology for spatial and temporal data (Rasmussen et al. 2007; Zhu et al. 2008; Aukema et al. 2010). During a visit to Academia Sinica in Taiwan, I worked with Drs. H.-C. Huang and J.-P. Wu on a spatio-temporal random field model for binary data with application to outbreaks of southern pine beetles (Zhu et al. 2005). The modeling framework is an extension of the autologistic model for purely spatial data on a lattice. My collaborators and I adapted the model for quantifying spatio-temporal patterns of mountain pine beetle outbreak in Western Canada (Aukema et al. 2006; Aukema et al. 2008; Zhu et al. 2008). Furthermore, recognizing that practical statistical tools were limited for complex spatial and spatio-temporal data that are not necessarily normal, I developed new statistical methodologies such as a latent variable model that has generalized linear models for the response variables and a spatio-temporal multivariate process for the latent variables (Zhu et al. 2005), continuous-time models (Rasmussen et al. 2007), and general modeling frameworks for spatio-temporal binary data while addressing challenging computational issues (Zheng and Zhu 2008).

Animal Movement Models:

I have been collaborating with Drs. K. Crooks, S. Magle, and J. Tracey in Wildlife Ecology on the behavior and conservation of wildlife. One research project concerns the conservation of mountain lions and other large mammals in southern California where the animals’ territories are threatened by rapid urban sprawl. We quantified animal movement paths in terms of the angle and length of each move across landscape features over time by developing statistical nonlinear regression models and inference. In the beginning, we considered the situation of one animal responding to one type of landscape feature and extended the traditional circular statistics to accommodate explanatory variables such as distance to a landscape feature (Tracey et al. 2005). We continued to extend the work to the situation of one animal responding to multiple types of landscape features, as well as from individual animal based inference to population-based inference using artificial neural network (Tracey et al. 2011 ) and finite mixture models (Tracey et al. 2013). In another research project, we studied prairie dogs in the front range of Colorado, comparing prairie dogs in urban areas and those in rural areas using linear regression and logistic regression analysis (Magle et al. 2005) and assessing the impact of human activities on the colonization and extirpation of prairie dogs over time (Magle et al. 2010). Most recently we developed new tools for inference and visualization of space use in 3D based on movement data (Tracey et al. 2014; R mkde package).

Teaching

The three courses I teach regularly are Statistics 571-Statistical Methods for Bioscience I, Statistics 572-Statistical Methods for Bioscience II, and Statistics 575-Statistical Methods for Spatial Data. My objective in Stat571 is to provide research-oriented students in the agricultural, biological, and environmental sciences with a thorough grounding in the basic statistical methods. My teaching philosophy is to stress an understanding of the procedures along with applications. While keeping the mathematical complexities to a minimum, I give considerable attention to the analysis of real data. I view the development of the ability to interpret results and to evaluate critically the methods used as of paramount importance. My objective in Stat572 is to provide students in bioscience with a thorough understanding of modern statistical procedures. Like in Stat571, I emphasize underlying concepts rather than an extensive coverage of a wide range of topics. To a large extent the assignments involve the analysis of data sets that approach the real-world complexity of data encountered in research and substantial use is made of the computer in conducting such analyses. The course Stat575 is directed towards graduate students who are interested in analyzing spatial data, including students from the environmental and ecological sciences, urban and regional planning, soil sciences, plant and animal sciences, and statistics. Similar to Statistics 571 and 572, I focus mostly on statistical methods and stress an understanding of the underlying concepts, as opposed to simply providing a cookbook of statistical formulas.

In addition, I have taught the following graduate-level statistics courses: STAT701 (3 Cr) Applied Time Series Analysis, STAT992 (3 Cr) Statistics for Spatial Data: Theory and Methods, and STAT998 (3 Cr) Statistical Consulting. I am currently leading the curriculum modernization and educational innovation effort in the Department of Statistics. One of the on-going projects is to develop a two-course sequence STAT601-602 Statistical Methods I&II for a new professional degree program in statistics and suitable for graduate students with strong quantitative background.